The figure shows graphs of pressure (P) versu | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The ideal gas equation is given by $PV = nRT$.Since $n = \frac{m}{M}$ and density $\rho = \frac{m}{V}$,we can write $V = \frac{m}{\rho}$.Substitut

Vedclass · Accepted Answer

$T_1 > T_2$

Vedclass · Answer

(A) The ideal gas equation is given by $PV = nRT$.Since $n = \frac{m}{M}$ and density $\rho = \frac{m}{V}$,we can write $V = \frac{m}{\rho}$.Substituting this into the ideal gas equation: $P \left( \frac{m}{\rho} \right) = \left( \frac{m}{M} \right) RT$.Simplifying,we get $P = \left( \frac{RT}{M} \right) \rho$.This equation represents a straight line passing through the origin,$P = m' \rho$,where the slope $m' = \frac{RT}{M}$.Since the slope is directly proportional to temperature $T$ (for a given gas,$R$ and $M$ are constant),the line with the greater slope corresponds to the higher temperature.In the given graph,the slope of the line for $T_1$ is greater than the slope of the line for $T_2$.Therefore,$T_1 > T_2$.

The figure shows graphs of pressure $(P)$ versus density $(\rho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.

Similar Questions

The $PV$ versus $T$ graph for equal masses of $H_2$,$He$,and $O_2$ is shown in the figure. Choose the correct alternative.

$A$ certain amount of gas has a volume of $12 \, L$ at a pressure of $3 \, atm$. If the temperature remains constant,what pressure in $atm$ must be applied to reduce its volume to $9 \, L$?

What is an ideal gas? Write the state equation for an ideal gas. Write and explain the different laws relating to gases.

What is molar volume? Write its $SI$ unit.

The figure shows the volume $V$ versus temperature $T$ graphs for a certain mass of a perfect gas at two constant pressures of $P_1$ and $P_2$. What inference can you draw from the graphs?

Vedclass Test Series

Exam Paper Generator

Online Exam Module